Normal Curve

What Exactly is a Normal Curve?

A normal curve is going to be encountered a lot in this course, so it is important that you know how to recognize one, at least on a basic level.

A normal curve looks like the image to the left. It essentially looks like a large hump when data is represented. Usually, the data being represented is a histogram, so you might see that it is made up of bars, like the bottom image.

The average is represented by the dashed line in the middle of hump. In a perfect normal curve, the mean, or average, is also equivalent to the median and to the mode. HOWEVER, this is rarely perfect with real data. So generally it is best to assume that the center line represents only the mode and can approximate the average if it is a nearly perfect curve (like those shown here) unless you are told otherwise.

Why are Normal Curves so Common?

Anytime you are looking at a lot of data (a good sample size), you are more likely to see this normal curve (aka normal distribution). That is because there are more likely to be a lot of individuals (or measurements, it depends on what the variable is) near the average than on the extremes.

Let's look at a specific example. Think about height. If I took the height of every male in the cafeteria (I am choosing only males to make the data simpler for the example), would most people be extremely tall (Over  203 cm 0r 6ft, 8 inches)? No, most people would be toward the middle. Some would be taller, some shorter, but most are clustered near that average. The same, typically, will occur with any variable you are measuring - it could be time spent on homework, income of a town, etc.

Do Normal Curves All Look the Same?

No, not quite; there are a lot of commonalities across normal curves, but there can be some differences as well. Firstly, the variable being measured might be different (the variable on the x-axis).

Some normal curves are more spread out, some are narrower. You will be exposed to a wide variety of these curves, but the images on the left represent a good basic representation of the different kinds you will encounter.

Why Do These Different Curves Matter? Aren't All Normal Curves the Same?

No, unfortunately, the differences represented by this 'spread' are not just visual. There are numerical differences. Remember those things from statistics or other math classes that you remember calculating but never necessarily understood what they mean? Well here I am specifically talking about standard deviation. Standard deviation sounds scary, so I think it deserves its own section.